Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
The remainder when $2^{60}$ is divided by 5 equals
(a)0
(b)1
(c)2
(d)3
Answer
Answer (as printed): B
Explanation
$2^{60}=\left(2^{2}\right)^{30}=4^{30}$. When $n$ is even, $\left(x^{n}-a^{n}\right)$ is divisible by $(x+a)$. $$\begin{aligned} & \therefore\left(4^{30}-1^{30}\right) \text { is divisible by }(4+1) \\ & \Rightarrow\left(4^{30}-1\right) \text { is divisible by } 5 \Rightarrow\left(2^{60}-1\right) \text { is divisible by } 5 . \\ & \Rightarrow \text { On dividing } 2^{60} \text { by } 5, \text { we get } 1 \text { as remainder. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.